Icefluid interaction
Monday 2nd October 2017 to Friday 6th October 2017
09:00 to 09:35  Registration  
09:35 to 09:45  Welcome from David Abrahams (INI Director)  
09:45 to 10:30 
Hung Tao Shen (Other) River Ice – Process, Theory, and Mathematical Modeling
River ice research has largely been driven by engineering and environmental problems that concern society. These concerns have been on ice jam flooding, hydropower operation, inland navigation, winter time ecology, and the influence of ice on water quality. River ice phenomena include formation, evolution, transport, accumulation, deterioration, and dissipation of various forms of ice. These phenomena involve complex interactions between hydrodynamic, mechanical, and thermal processes, under the influence of meteorological and hydrological conditions as well as the operations of water resources engineering projects. Most of the river ice phenomena also occur in sea ice, except that river ice forms in freshwater confined within channels. Mathematical modeling of river ice processes faces similar problems as sea ice, but in much smaller spatial and time scales because of the strong boundary effects. There has been only a relatively small group of researchers engaged in this no ntraditional topic of river hydraulics. However, important advances have been made in the last couple of decades. In this presentation, river ice processes and major research advances enabled by mathematical modeling will be discussed. These will include frazil and anchor formation, surface ice transport and ice jam dynamics, undercover frazil jam/hanging dam evolution, breakup processes, and sediment transport with ice effects. Keywords: River ice, freeze up, frazil ice, ice jams, breakup, hydrodynamics, mathematical modeling 
INI 1 
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Mike Meylan (University of Newcastle, Australia) tba 
INI 1 
11:45 to 12:30 
Stefanie Rynders (University of Southampton) Modelling dynamics of the marginal ice zone, including combined collisional and EVP rheology
Coauthors: Yevgeny Aksenov (National Oceanography Centre), Daniel Feltham (Centre for Polar Observations and Modeling, University of Reading), George Nurser (National Oceanography Centre) Exposure of large, previously icecovered areas of the Arctic Ocean to the wind and surface ocean waves results in the Arctic pack ice cover becoming more fragmented and mobile, with large regions of ice cover evolving into the Marginal Ice Zone (MIZ). The need for better climate predictions, along with growing economic activity in the Polar Oceans, necessitates climate and forecasting models that can simulate fragmented sea ice with greater fidelity. The main focus here is on sea ice rheology. A Combined Collisional, reflecting the granular behaviour of MIZ sea ice, and ElasticViscousPlastic (EVP) rheology is implemented in an idealised and a global sea iceocean model. The effect of surface waves on ice motion is included in the turbulent kinetic energy or ‘granular temperature’ of ice floes. The granular temperature is validated with accelerometer data. It is found that the combined rheology has impact beyond the marginal ice zone, influencing ice motion and sea ice thickness. Taking into account the fragmented nature of MIZ ice also allows for another dynamical feature of the MIZ: in idealised channel model simulations ice edge jets occur when variable floe size is used. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/20072013) under grant agreement n° 607476. 
INI 1 
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Vernon Squire (University of Otago) Philosophical ramblings about models and observations in waveice interactions
The focus of this talk will be on the two research strands that
currently exemplify waveice interaction research, namely: (i) the continuum paradigm,
which leads naturally into parametrizations that can potentially be
incorporated straightforwardly into wave forecasting models such as WAVEWATCH
III or global climate models; and (ii) methodology that endeavours to represent
the physics of each constituent process as faithfully as possible, acknowledging
from the outset that approximations are inevitable. The advantages and
disadvantages of each approach will be discussed, especially in the context of
implications for the design of field experiments and the subsequent analysis of
any data collected. It is asserted that field experiments grounded in the continuum
paradigm are particularly challenging because the number of degrees of freedom
in Nature is huge compared with a typical model. The consequences of using a
linear ansatz will also be made clear, recognizing that very nearly all current mathematical models of the phenomenon
are linear yet the few data that are available suggest that the assumption of
linearity is inconsistent with observation in some cases and presupposes
outcomes that are too restrictive.

INI 1 
14:15 to 15:00 
John Grue (University of Oslo) tba 
INI 1 
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
Elizabeth Hunke (Los Alamos National Laboratory) tba 
INI 1 
16:15 to 17:00 
Aleksey Marchenko (Norwegian University of Science and Technology) tba 
INI 1 
17:00 to 18:00  Welcome Wine Reception at INI 
09:00 to 09:45 
Luke Bennetts (University of Adelaide) Modelling water wave overwash of ice floes
I will summarise progress towards modelling wave overwash of ice floes, which (after breakup) is arguably the most important nonlinear phenomenon in wave–ice interactions, and certainly the most striking one. The phenomenon is unique to wave–ice interactions, occurring because the small freeboards of ice floes allow waves with relatively modest (nonextreme) amplitudes to wash over their upper surfaces when differential motion between the floe and the surrounding wave field exists. Overwash impacts floes thermodynamically, and dissipates wave energy, thus reducing the distances waves penetrate into the icecovered ocean. From a mathematical modelling perspective, it is a highly nonlinear phenomenon, meaning it cannot be captured by standard perturbation techniques. I will present a bespoke overwash model, along with supporting laboratory experiments and numerical CFD simulations. Applying the methodology to simplified versions of the problem will be shown to provide insights into model performance.
Coauthors: David Skene (Uni Adelaide); Michael Meylan (Uni Newcastle); Alessandro Toffoli (Uni Melbourne); Filippo Nelli (Swinburne Uni Tech); Kevin Maki (Uni Michigan) 
INI 1 
09:45 to 10:30 
Emilian I Parau (University of East Anglia) tba 
INI 1 
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Olga Trichtchenko (University College London) tba 
INI 1 
11:45 to 12:30 
Philippe Guyenne (University of Delaware) Numerical study of solitary wave attenuation in a fragmented ice sheet
Coauthor: Emilian Parau (University of East Anglia) A numerical model for phaseresolved simulation of nonlinear ocean waves propagating through fragmented sea ice is proposed. This model solves the full timedependent equations for nonlinear potential flow coupled with a nonlinear thinplate formulation for the ice cover. The coefficient of flexural rigidity is allowed to vary spatially so that distributions of ice floes can be directly specified in the physical domain. Twodimensional simulations are performed to examine the attenuation of solitary waves by scattering through an irregular array of ice floes. 
INI 1 
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Pat Langhorne (University of Otago) In situ detection of fluid movement in Antarctic landfast sea ice
Coauthors: Pat Wongpan (University of Otago), Ken Hughes (University of Otago & University of Victoria), Inga J, Smith (University of Otago) Vertical temperature strings are used in sea ice research to study heat flow, ice growth rate, and oceaniceatmosphere interaction. We demonstrate the feasibility of using temperature fluctuations as a proxy for fluid movement, a key process to resupply nutrients to Antarctic landfast sea ice algal communities. Four thermistor arrays (including two midwinter records) were deployed in the landfast sea ice of McMurdo Sound, Antarctica. By smoothing temperature data with the robust LOESS method, we obtain temperature fluctuations that cannot be explained by insolation or heat loss to the atmosphere. Statistical distributions of these temperature fluctuations are investigated with sensitivities to the distance from the iceocean interface, average ice temperature, and sea ice structure. Temperature fluctu ations are discrete events that have greatest magnitude close to the iceocean interface (< 50 mm) at temperatures > −3 &# x25E6;C. At temperatures > −3 ◦C fluctuations occur for 43% of the time, when the ice is colder (−3 to −5 ◦C) this active period is reduced to 11%. Assuming temperature fluctuations occur at a critical Rayleigh number derived from mushy layer theory, we parameterise a measure of permeability of this thick (>1 m) Antarctic landfast sea ice in terms of average ice temperature. This permeability decreases by three orders of magnitude between the iceocean interface and ∼70 mm above it, as the sea ice temperature changes from the freezing point to −5 ◦C. The same permeability parameterisation is independent of whether the sea ice has a columnar crystal structure or has a more disordered platelet ice structure, characteristic of proximity to an ice shelf. 
INI 1 
14:15 to 15:00 
Hayley Shen (Clarkson University) Wave Propagation in Viscoelastic Materials over Water
Ice
covers over water modify the mass, energy, and momentum transfer between the
atmosphere and ocean. Ocean wave propagation is one of the numerous topics from
these three basic processes. Because of the Arctic ice reduction, longer fetch
has increased both the intensity and the dominant wave period. Longer period
waves damp much less. They thus propagate further into ice covers. The contemporary
Arctic system cannot be properly evaluated without a good grasp of the growing
presence of waves under ice covers. Ice covers are complex materials. Even a
continuous solid ice cover does not fit into a simple constitutive model. In
the field ice covers often are consisted of discontinuous pieces of various
sizes and shapes, mixed with open water or slurry of ice crystals. Such a
composite cover has been idealized as a linear viscoelastic material. This
hypothesis is based on a simple physical argument: all materials under
deformation simultaneously store some and dissipate some energy. The first order
approximation is therefore a linear viscoelastic model. To test this hypothesis,
the dominant characteristics of the model must be thoroughly understood. The
most important characteristic of wave propagation is the dispersion relation.
Even with a simple linear viscoelastic model, the dispersion relation is
complicated. There are many roots all satisfy the dispersion relation. All of
them may be present under different conditions. In this talk, a description of
these roots and their physical meanings will be presented. Their presence has
been found in other fields. Knowledge from other fields may shed light on how
these different wave modes interact under different situations.

INI 1 
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
JeanMarc VandenBroeck (University College London) tba 
INI 1 
16:15 to 17:00 
Andrej Il’ichev (Steklov Mathematical Institute, Russian Academy of Sciences) Wave patterns beneath an ice cover
We prove existence of the solitonlike solutions of the full system of equations which describe wave propagation in the fluid of a finite depth under an ice cover. These solutions correspond to solitary waves of various nature propagating along the waterice interface. We consider the planeparallel movement in a layer of the perfect fluid of the finite depth which characteristics obey the full 2D Euler system of equations. The ice cover is modeled by the elastic KirchgoffLove plate and it has a considerable thickness so that the plate inertia is taken into consideration when the model is formulated. The Euler equations contain the additional pressure arising from the presence of the elastic plate freely floating on the liquid surface. The mentioned families of the solitary waves are parameterized by a speed of the wave and their existence is proved for the speeds lying in some neighborhood of its critical value corresponding to the quiescent state. S olitary waves, in their turn, bifurcate from the quiescent state and lie in some neighborhood of it. By other words, existence of solitary waves of sufficiently small amplitudes on the waterice interface is proved. The proof is conducted with the help of the projection of the required system to the central manifold and further analysis of the resulting reduced finite dimensional dynamical system on the central manifold.

INI 1 
09:00 to 09:45 
Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics); (Novosibirsk State University) tba 
INI 1 
09:45 to 10:30 
Mariana Haragus (Université de FrancheComté) Stability criteria for nonlinear waves in Hamiltonian and reversible systems
We present two general stability/instability criteria for nonlinear waves in Hamiltonian or reversible systems. Both criteria rely upon spectral properties of the linear operators found by linearizing the system at a given wave. We apply these results to some model equations arising in waterwave problems. The focus is on the question of transverse stability/instability of periodic traveling waves. 
INI 1 
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Timothy Williams (Natural Environment Research Council (NERC)) A sea ice model with waveice interactions on a moving mesh
Timothy Williams, Pierre Rampal, Einar Olason, Syvain Bouillon and Abdoulaye Samake The neXtSIM (neXt generation Sea Ice Model) sea ice model runs the MaxwellEB rheology solved with finite element methods on a triangular mesh. It also has thermodynamic effects and a slab ocean included beneath, as well as waveice interactions (ice breakup by waves, ice drift due to the wave radiation stress). An ALE (Arbitrary Lagrangian/Eulerian) scheme has now been implemented in neXtSIM, so that the mesh is usually moving as time goes on. As part of an investigation about the best strategy for coupling the wavesinice module (WIM) to neXtSIM, the WIM may now be run on the neXtSIM mesh. In this talk we give an overview of both neXtSIM and the WIM, and also some results comparing the different coupling strategies for the WIM. 
INI 1 
11:45 to 12:30 
Yevgeny Aksenov (National Oceanography Centre, Southampton) Impacts of ocean waves on the Polar Sea Ice and Oceans
Coauthors: Lucia Hosekova (University of Reading, UK), Danny Feltham (University of Reading, UK), Tim Williams (Nansen Environmental and Remote Sensing Center (NERSC), Norway), A.J. George Nurser (National Oceanography Centre, UK), Gurvan Madec (Institut Pierre Simon Laplace (IPSL), France), Andrew Coward (National Oceanography Centre, UK) We examine effects of ocean surface waves on the polar sea ice and ocean using a sea iceocean general circulation model NEMO (stands for Nucleus for European Modelling of the Ocean) coupled with the ocean wave model WAM output from model of the European Centre for MediumRange Weather Forecasts (ECMWF). In the model the waveice interactions include: ice fragmentation due to break–up by waves in the vicinity of the ice edge; wave attenuation due to multiple scattering and nonelastic losses in the ice, wave advection and evolution of ice fragmentation. We analyse the impact of the waves on sea ice and the upper ocean, focusing on the marginal ice zone (MIZ) where the wave impacts are the most. The study compares the model results with the observations, and highlights a need to farther theoretical understanding of sea ice fragmentation and summarise requirements for observational techniques. The study was carry out in the EU FP7 Project ‘Ships and waves reaching P olar Regions (SWARP)’. 
INI 1 
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 17:00  Free Afternoon 
09:00 to 09:45 
Pietro Baldi (Università degli Studi di Napoli Federico II) Time quasiperiodic gravity water waves in finite depth
We consider the water wave equations for a 2D ocean of finite depth under the action of gravity. We present a recent existence and linear stability result for small amplitude standing wave solutions that are periodic in space and quasiperiodic in time. The result holds for values of a normalized depth parameter in a Cantorlike set of asymptotically full measure. The main difficulties of the problem are the presence of derivatives in the nonlinearity (the system is quasilinear), and a small divisors problem where the frequencies of the linear part grow in a sublinear way at infinity (like the square root of integers). To overcome these problems we first reduce the linearized operators (which are obtained at each approximate quasiperiodic solution along a NashMoser iteration) to constant coefficients up to smoothing operators, using pseudodifferential changes of variables that are quasiperiodic in time. Then we apply a KAM reducibility scheme which requires very weak second Melnikov nonresonance conditions (losing derivatives both in time and space). Such nonresonance conditions are sufficiently weak to be satisfied for most values of the normalized depth parameter, thanks to arguments from degenerate KAM theory. Joint work with Massimiliano Berti, Emanuele Haus and Riccardo Montalto. 
INI 1 
09:45 to 10:30 
Mark Groves (Universität des Saarlandes); (Loughborough University) tba 
INI 1 
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Thomas Folegot (QuietOceans) tba 
INI 1 
11:45 to 12:30  TBA  INI 1 
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Stephen Ackley (University of Texas at San Antonio) Antarctic Coastal Polynyas: Do Measurements of Winter Processes give clues to modeling Improvements and better model fidelity?
The PIPERS cruise to the Terra Nova Bay (TNB) and Ross Ice Shelf (RIS) polynyas during AprilJune 2017 focused on joint measurements of airiceocean wave interaction in these polynyas. In Terra Nova Bay, measurements were taken during intense katabatic wind events with sustained winds over 35 meters per second and air temperatures of 15C or below. Despite a relatively short fetch, intense wave fields with wave amplitudes of over 2m and 79 sec periods built and large amounts of frazil ice crystals grew. The frazil ice gathered initially into short plumes that eventually were added laterally to create longer, wide streaks. The wave field within the wider streaks was dampened and enhanced the development of pancake ice. Eventually, the open water areas sealed off between the streaks, developing a uniform pancake ice cover of 100 percent concentration. The pancakes continued to grow in diameter and thickness, further attenuating the wave field and the pancake ice growt h then ceased. While the waves died off however, katabatic wind velocities were sustained and resulted in a wide area of concentrated, rafted, pancake ice that was rapidly advected downstream until the end of the katabatic event. The equilibrium thickness of the ice was typically 30 to 40 cm in the pancake ice. High resolution TerraSarX radar satellite imagery showed the length of the ice area produced in one single event extended over 300km or ten times the length of the open water area during the polynya event. The TNB polynya is therefore an “ice factory” where frazil ice is manufactured into pancake ice floes that are then pushed out of the assembly line and advected, rafted and occasionally piled up into “dragon skin” ice, until the katabatic wind dies off at the coastal source.

INI 1 
14:15 to 15:00 
Alena Malyarenko (University of Otago) Interactions between phase change and boundary layer structure
Coauthors: Pat Langhorne (University of Otago), Natalie Robinson (NIWA), Mike Williams (NIWA) Thermodynamic ice ablation includes both melting and dissolving of the ice. Existing parametrisations are usually based on the 3equation model, with equations that describe heat and salt flux balances together with the freezing point equation for sea water. However, these equations do not represent both melting and dissolving conditions, or the transition between these conditions. Nor do the 3 equations represent well the two dominant velocity regimes: sheardriven and buoyancydriven mixing. Turbulent heat and salt transfer coefficients need to reflect the variety of boundary layer structures that can form under different velocity and temperature regimes. Here the different conditions and velocity regimes are considered in the in context of multiyear observations of temperature, velocity and ablation rate from under the Ross Ice Shelf. These observations of a dissolving ice shelf in subzero conditions can be used to constrain transitions from buoyancydriven mixing to sheerdriven mixing. While these observations are under an ice shelf they are expected to scale to the higher salinities found in sea ice. 
INI 1 
15:00 to 15:30  Afternoon Tea  
15:30 to 16:15 
Jorma Kämäräinen (Finnish Transport Safety Agency) tba 
INI 1 
16:15 to 17:00  Discussions  INI 1 
19:30 to 22:00  Formal Dinner at Robinson College 
09:00 to 09:45 
Frank Thomas Smith (University College London) Shear flow over patches of flexible surface and related nearsurface interactions
Shear flow over a threedimensional hydroelastic surface patch or patches is considered here, modelling the interactive effects encountered well within an incident atmospheric or seawater boundary layer. The configuration has a finite patch or an array of patches of flexible surface which are sited in an otherwise quasifixed solid surface. The scaled viscousinviscid response depends on the shear, the viscosity and therefore the vorticity, as well as icepatch parameters and threedimensionality. Related modelling of debris, particle and iceshard movements involves fluid/body interaction. Analysis and computations on linear and nonlinear effects often leading to flow transition are to be described.

INI 1 
09:45 to 10:30 
Manish Tiwari (University College London) tba 
INI 1 
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Henrik Kalisch (Universitetet i Bergen) tba 
INI 1 
11:45 to 12:30 
Ying Gou (Dalian University of Technology) Experimental study on dead water resistance of ice floe in a twolayer fluid
Coauthor: Bin Teng (University of Technology) The dead water phenomenon is well known that when a boat is sailing on a twolayer fluid, there is an extra resistance due to the wave generating at the interface. Here, we investigate the dead water resistance of a ice floe instead of slender streamline body by threedimensional towing experiments. The lengthwidth ratio of ice floe is 1.5. The dimensionless ice floe draught d/h1 is varied from 0.5 to 1.0, where h1 is the upper layer depth. The Froude number Fr=U/c0 is in the range 0.3~1.3 (U towing speed, c0 the linear internal long wave speed). The experiment results show that dead water coefficient Cdw and function Cdw/(d/h1)2 attains a maximum at subcritical Froude number, Fr≈0.5~0.6, which is smaller than the previous results of slender ship. For relative small draughts, Cdw/(d/h1)2 depends on the Froude number only in the range close to critical speed (Fr>0.85), irrespective of the draught, which is same with the previous observations. But this conclusion is not applied for the case d/h1=1.0. The different variation tendency of Cdw/(d/h1)2 versus Fr is observed here. That means an extended study should be continued for deeper draught cases. 
INI 1 
12:30 to 13:30  Lunch @ Wolfson Court  
13:30 to 14:15 
Johannes E. M. Mosig (University of Otago) Degrees of freedom in the marginal ice zone's waveice system
The marginal
ice zones (MIZs) in both the Arctic and Southern Oceans play a key role in the
Earth's climate system and the impact of sea ice on wave propagation is
important to understand in order to create reliable wave forecasting models. To
create efficient and accurate models of the MIZ's waveice system one must
first identify the degrees of freedom that are relevant for such a model. In my
PhD thesis and in this presentation, I will illuminate aspects of three
commonly pursued paradigms: (i) floe models, where the degrees of freedom are
comprised of individual ice floes; (ii) effective material models such as the
one proposed by Wang and Shen (2010, dx.doi.org/10.1029/2009JC005591); and
(iii) energy transport models, where the relevant degree of freedom is a single
scalar field—the wave intensity—defined over the horizontal ocean domain.
Throughout this talk I will touch upon various mathematical and computational techniques which have very general applications, yet are rarely used by the wave and sea ice community. Specifically, I use the method framework of generalized polynomial chaos to investigate the propagation of uncertainties in various models. Moreover, I attempt to derive an analytical relationship between local scale potential flow theory, and the largescale transport equation description of the MIZ, using a multiscale expansion and a Wigner transform of the amplitude envelope of a propagating wave package. Supervisors: Vernon A. Squire, Fabien Montiel Publications: Mosig et al., Comparison of viscoelastictype models for ocean wave attenuation in icecovered seas, 2015, dx.doi.org/10.1002/2015JC010881 Mosig et al., Water wave scattering from a mass loading ice floe of random length using generalised polynomial chaos, dx.doi.org/10.1016/j.wavemoti.2016.09.005 
INI 1 
14:15 to 15:00 
Usama Kadri (Cardiff University); (Massachusetts Institute of Technology) On acousticgravity waves in arctic zones with elastic icesheets
We present an analytical solution of the boundary value problem of propagating acousticgravity waves generated in the ocean by earthquakes or icequakes in arctic zones. At the surface, we assume elastic icesheets of a variable thickness, and show that the propagating acousticgravity modes have different mode shape than originally derived by Ref. [1] for a rigid icesheet settings. Computationally, we couple the icesheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented icesheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depthintegrated equation valid for spatially slowly varying thickness of icesheet and water depth. Surprisingly, and unlike the freesurface setting, here it is found that the higher acousticgravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. icesheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acousticgravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation.

INI 1 
15:00 to 15:30  Afternoon Tea 